Tensor products and spaces of vector-valued continuous functions

Quasibarrelled, barrelled and bornological tensor products of locally convex spaces are studied. A device, called the desintegration lemma, is developed for the most difficult case, that of the injective topology. Applications are given to spaces of vector-valued continuous functions.Both authors thank the Volkswagenstiftung and the A. von Humboldt Stiftung. The second author is a research associate of the Belgian National Fund for Scientific Research N.F.W.O.